I know in ours a set number of parents can require the board to call a "special" meeting and as long as notification, quorum, etc. is met the meeting can be held (by the board with parent input) and board members can be removed, with or without cause, by a 2/3's membership approval.
Otherwise the next PTO election (which should be in the by-laws) have other members run for the positions and be elected in.
The question you need to ask yourself first though is if your by-laws allowed by election of officers/board why did no one run or win the election for those positions at the prior election? Do you have enough people willing to step up and do the jobs? Do you have enough support from the membership or just from a select few?
There are no quick and easy ways to remove one board member much less an entire board. I take it that your PTO's by-laws contain no term limits? How much authority per the by-laws is the principal or school given over the board's activities?
I suggest you post your situation with the pertinent details on the Robert's Rules of Order forum for expert assistance. Here is the link:
Our PTO has become ineffective due to our Executive Board. They have all been in office too long and have lost sight of the goal of PTO. They have run off every volunteer with rudeness and negativity and spend the PTO money on dinners and things that don't help the students or our school. We have a brand new principal this year and I'm not sure he knows how to deal with them. There are plenty of parents who volunteer at the school ... we just don't know how to oust the current officers. Any suggestions would be greatly appreciated.